基于微分求积法及 V－变换的大规模动力系统快速数值计算方法

摘要

针对大规模动力系统动态响应的数值计算，传统的微分求积法通常在时间域上逐步离散、整体求解，存在“维数灾”问题。在多级高阶时域微分求积法的基础上，提出了基于 V －变换的大规模动力系统动态响应的快速数值计算方法。利用微分求积法的加权系数矩阵满足 V －变换这一重要特性，将离散后的雅可比矩阵方程进行解耦分块，推导形成了多级分块递推计算方法。数值算例表明，即使采用相当于 Newmark 方法2s 倍的步长，微分求积法的计算精度仍比Newmark 方法要高出2～3个数量级。进一步对3个不同规模的算例系统进行了测试，结果表明：相对于传统的数值计算方法，多级分块递推计算方法可以获得较大的加速比，能够显著提高大规模动力系统动态响应的计算效率。%For numerical simulation of large-scale dynamic systems'response,the traditional differential quadrature method (DQM)usually adopts successively discrete and global solution in time domain,where there is the problem of“curse of dimensionality”.On the basis of the multi-stage high-order time domain differential quadrature method,a fast numerical calculation method for large-scale dynamic systems'response based on V-transformation was proposed.Using the V-transformation processed by the weighting coefficient matrix of DQM,the whole Jacobian matrix equations involved in the traditional approach of DQMwere decoupled into blocks,thus a multi-stage block recursive method was achieved.The numerical examples show that,even using a step size of 2s times that as high as in the Newmark method,the calculation precision of the differential quadrature method is about 2 ~3 orders higher than that of the Newmark method.Furthermore, three different scale systems were used for computational efficiency test and the results show that the multi-stage block recursive method can obtain high speedup compared with the traditional numerical methods,which can significantly improve the computational efficiency of large-scale dynamic systems'response.